Particle moving inside a rotating hollow tube

The hollow tube is pivoted about a horizontal axis through point O and is made to rotate in the vertical plane with a constant counterclockwise angular velocity θ'=3rad/s. If a 0.1-kg-particle is sliding in the tube toward O with a velocity of 1.2 m/s relative to the tube when the position θ=30 degrees is passed, calculate the magnitude N of the normal force exerted by the wall of the tube on the particle at that instant.

2. Relevant equations

Newtons second law.

3. The attempt at a solution

I decided to work with polar coordinates for this problem and therefore I have drawn two unit vectors, e_(r) and e_(θ), where e_(r) is along the tube(away from O) and e_(θ) is perpendicular to e_(r).

We know that θ'=3rad/s and that v=r'=-1.2m/s since the particle is moving towards O. It follows that r''=0 since r' is constant.

I have drawn a free-body diagram and for the particle there is:

A force mgcosθ in the negative e_(θ) direction, a normal force N(Isn't there a frictional force too?But I have neglected it since no information is given about it).

Since it doesn't move in the e_(θ)-direction it means that N=mgcosθ. Now I try to use it in Newton II:

F_(r)=ma_(r)=m(r''-r(θ'^2)) but I do not know how to proceed.1. The problem statement, all variables and given/known data